Table lfunc_lfunctions
L-functions
{'Lhash': '937175545133297732714533819121', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5683861588601082, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.7376988373270414, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.676937174416252, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5683861588601082, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.7376988373270414, 0], [7.0, 0]], [[1.0, 0], [-0.3605318730741954, 0], [11.0, 0]], [[1.0, 0], [-5.261228602844426, 0], [13.0, 0]], [[1.0, 0], [-0.37085217822910244, 0], [17.0, 0]], [[1.0, 0], [-4.605855206350555, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.9392383370892107, 0], [29.0, 0]], [[1.0, 0], [9.666616869261345, 0], [31.0, 0]], [[1.0, 0], [-3.268615948696702, 0], [37.0, 0]], [[1.0, 0], [-5.299770210163406, 0], [41.0, 0]], [[1.0, 0], [0, 0], [43.0, 0]], [[1.0, 0], [-1.2549138168206828, 0], [47.0, 0]], [[1.0, 0], [-10.927845472105771, 0], [53.0, 0]], [[1.0, 0], [-9.669549828563975, 0], [59.0, 0]], [[1.0, 0], [-9.7144062219067, 0], [61.0, 0]], [[1.0, 0], [-7.070009408237164, 0], [67.0, 0]], [[1.0, 0], [11.374708305144301, 0], [71.0, 0]], [[1.0, 0], [-0.7450861831793173, 0], [73.0, 0]], [[1.0, 0], [0.4157085715718258, 0], [79.0, 0]], [[1.0, 0], [-9.268615948696702, 0], [83.0, 0]], [[1.0, 0], [-12.612169992374298, 0], [89.0, 0]], [[1.0, 0], [-14.040402006793078, 0], [97.0, 0]], [[1.0, 0], [12.744013623350785, 0], [101.0, 0]], [[1.0, 0], [-3.3134723420394256, 0], [103.0, 0]], [[1.0, 0], [-8.131843630976485, 0], [107.0, 0]], [[1.0, 0], [5.795078673516718, 0], [109.0, 0]], [[1.0, 0], [7.607241305630568, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20288192, 'index': 6, 'label': '2-1840-1.1-c1-0-6', 'leading_term': '1.2810662912652358593202170805939', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1840/2/a/v/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.281066291265236, 1.2739797484789326, 1.252600662731041, 1.216581489894217, 1.1653782438390388, 1.0983005707475415, 1.0145766736176702, 0.9134287979696665, 0.794154771399234, 0.6562112722724749, 0.4992949432812499, 0.3234180169302345, 0.12897566759117893, -0.08319721861305365, -0.3117817807092006, -0.5549450475677942, -0.8103252975617968, -1.0750340395818203, -1.3456754802725552, -1.6183840341056293, -1.8888800617377852, -2.1525435816702103, -2.404505193115407, -2.6397528844371876, -2.853252798106196, -3.040081401370644, -3.195565897143745, -3.3154291299547034, -3.3959347266705664, -3.4340277908231043, -3.4274661715599253, -3.374937180030388, -3.2761546504118164, -3.131931457931033, -2.9442230242110603, -2.71613796594616, -2.45191287301816, -2.1568492246192132, -1.8372116454193825, -1.500088037721683, -1.1532135603794937, -0.8047619133771341, -0.46310887384800115, -0.1365744551193345, 0.16684863788549212, 0.4397714697027978, 0.6756806006254811, 0.8691948699908092, 1.01629682765778, 1.114528599701572, 1.1631425901818337, 1.163198467658627, 1.1175993554148398, 1.0310620118105864, 0.9100180062652515, 0.7624454024694151, 0.5976331712127338, 0.4258833726419184, 0.2581589611550803, 0.1056877560441491, -0.0204644361840081, -0.10983648867795567, -0.1530137634451043, -0.14205141715477096, -0.07086123300760615, 0.06445558085041034, 0.2653460054834474, 0.5306276654964938, 0.8564078612482946, 1.236107556605755, 1.6605947730011914, 2.1184274829939898, 2.5962014734941286, 3.0789939488657208, 3.550889072175171, 3.995567411618518, 4.396937579810962, 4.739785425661406, 5.010414139626469, 5.197247709099375, 5.2913704165383715, 5.286976565088626, 5.181707346826915, 4.976855681160155, 4.677424829973552, 4.292032469129034, 3.8326584375318524, 3.3142413249537737, 2.7541360933418972, 2.1714517269461306, 1.586294140743211, 1.0189449197758114, 0.48901061514244065, 0.014580028266493203, -0.3885720264587513, -0.7076967094858093, -0.9336636688676845, -1.0614031864535773, -1.0901730595816457, -1.0236327556120635, -0.869715953166975, -0.6403019293756501, -0.35069593780642555, -0.01893828050944221, 0.33502927252525316, 0.6903031959878222, 1.0260211894298616, 1.322381122386171, 1.5616264117871896, 1.728948478978167, 1.8132596098854934, 1.807794674899277, 1.7105075858334025, 1.5242377801198501, 1.2566330145259665, 0.919826809171505, 0.5298814170023057, 0.10601956434147719, -0.33032024228156726, -0.7565599585966937, -1.1501368676668504, -1.4896786452397743, -1.7561376357693301, -1.9338239485884219, -2.011280824342474, -1.9819527053758197, -1.8446062962366627, -1.603477180259868, -1.2681286739417539, -0.8530248382926024, -0.37683512340523123, 0.138496849444311, 0.6688742138470873, 1.189299868017032, 1.6751953608662913, 2.1037143203587867, 2.4549778129736604, 2.7131617838333604, 2.867373490581265, 2.9122643457486563, 2.848340334596813, 2.6819474878888503, 2.4249279011726137, 2.0939605170521216, 1.7096192643748085, 1.2951981040853764, 0.8753670400267537, 0.47473429905013564, 0.11639692159758631, -0.17943559707522774, -0.39666248500489953, -0.5242829694218886, -0.5570949339023021, -0.49605425690751803, -0.34826731802280847, -0.12661045622184008, 0.1510076422252076, 0.4627028673084663, 0.7839341140233844, 1.0890083532412236, 1.3526845284337072, 1.5517805090657997, 1.666684997522161, 1.6826798652595099, 1.5909878260246622, 1.389475219189612, 1.0829592080245536, 0.6830918198426699, 0.20781863852256438, -0.3195639019093844, -0.8717033776987607, -1.4187662798789387, -1.9302019019528804, -2.376590392592887, -2.7314625824561336, -2.9729784364529612, -3.085357260042374, -3.059965883884558, -2.8959903134451763, -2.6006407001036442, -2.1888675579067427, -1.682597233758049, -1.1095248850232602, -0.5015317154173492, 0.10718188175067586, 0.6821359908840194, 1.1906593735610755, 1.603896542330827, 1.8986068034610581, 2.0586392517032754, 2.075986204047757, 1.951342653676725, 1.6941295337279272, 1.3219720605182195, 0.8596590796573798, 0.3376429436456376, -0.20983019807334616, -0.7468447566787488, -1.238061742386433, -1.650943836816583, -1.9578163124013392, -2.1376294191078085, -2.17730560636315, -2.0725806281137555, -1.8282796355229505, -1.4580057824954074, -0.9832573095043072, -0.4320270044034031, 0.16302717789262436, 0.7667221098074691, 1.3436599337075563, 1.860555955861272, 2.2884282876023363, 2.604501294333135, 2.793692792823196, 2.8495818789803153, 2.77478858009954, 2.5807359797566356, 2.286807438294251, 1.9189531841220249, 1.5078390080857085, 1.0866623508644149, 0.6887853872945436, 0.345348967189588, 0.08303432216418236, -0.07786909471726688, -0.12495098898038182, -0.05461386722388302, 0.12761828057350713, 0.40744422856299756, 0.7627648499348846, 1.1652345176587755, 1.5822802065812922, 1.979449413495771, 2.3229228725706084, 2.582014217314997, 2.7314773881520527, 2.7534539976521377, 2.6389164269254928, 2.3884966391803126, 2.0126332726058265, 1.5310175866982134, 0.9713689145666293, 0.3676188427638018, -0.24237312783845463, -0.8194144145052692, -1.3257023190084622, -1.72748130215601, -1.997443167310087, -2.1166951034879458, -2.0761498261270237, -1.8772323311377943, -1.5318462608388337, -1.0615961364948012, -0.4963159023415575, 0.12799462016361937, 0.7716794623798608], 'positive_zeros': ['0.73930114888484845428126629533039', '2.54526778852463296582397838949760', '3.50498762785343705309704084703974', '3.78412579682264420598315908340321', '5.45116032660235916260362165796020', '6.03835507846753314531492757951509', '6.86974555955036521775890010158039', '7.66031533688569428577097904331786', '8.693304939406647064969092670324458', '9.109959738712378489852191146317451'], 'prelabel': '2-1840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73930114888484845428126629533', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.54526778852463296582397838950', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.50498762785343705309704084704', 'prec': 100}}